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2 years ago

Find the exact sum of the arithmetic series 6+3.8+⋯−29.2

Mathematics

1 answer:

matrenka [14]2 years ago

5 0

Answer:

-197.2

Step-by-step explanation:

Since it is arithmetic series, first find the difference d between the two know series.

3.8 - 6 = - 2.2

d = -2.2

a = 6

Tn = -29.2

Looking for the n term, use the linear method.

Tn = a+( n - 1)d

Substitute all the parameters

-29.2 = 6+( n - 1 ) -2.2

-29.2 = 6 - 2.2n + 2.2

- 29.2 = 8.2 - 2.2n

-29.2 - 8.2 = - 2.2n

-37.4 = -2.2n

n = 37.4/ 2.2

n = 17 terms.

To Find the exact sum of the arithmetic series, use the sum formula below

Sm = n/2( 2a + (n - 1)d)

Sm = 17/2( 2 × 6 + ( 17 - 1 ) -2.2

Sm = 17/2(12 - 35.2)

Sm = 8.5( - 23.2)

Sm = - 197.2

Therefore, the exact sum of the arithmetic series is -197.2

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Answer:

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Step-by-step explanation:

* Lets explain how to solve the problem

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- The system of equation has one solution if at least one of the

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* Lets solve the problem

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- Lets simplify equation (2) by multiplying the bracket by 2

∴ y = 4x - 2

- The two equations have same coefficient of y and x and different

numerical terms

∴ They have zero equation

y = 4x + 2

y = 2(2x - 1)

Zero solutions.

4x + 2 can never be equal to 4x - 2

∵ y = 3x - 4 ⇒ (1)

∵ y = 2x + 2 ⇒ (2)

- The coefficients of x and y are different, then there is one solution

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∴ x - 4 = 2

- Add 4 to both sides

∴ x = 6

- Substitute the value of x in equation (1) or (2) to find y

∴ y = 2(6) + 2

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Step-by-step explanation:

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Answer:

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Answer:

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Step-by-step explanation:

We have to find equivalent expression to :

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We have to convert the the mixed fraction form $-2\frac{1}{4}$ to simpler $\frac{p}{q}$ fraction form.

Let us learn the concept first.

Mixed fraction is combination of a whole number and a fraction.

Expression of the form $a\frac{b}{c}$ have the following understanding:

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To convert mixed fraction to fraction we can use the following:

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